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CATEGORIES:Discrete Analysis Seminar
SUMMARY:Towards a calculus for nonlinear spectral gaps - A
ssaf Naor (Courant/Weizmann)
DTSTART;TZID=Europe/London:20090306T163000
DTEND;TZID=Europe/London:20090306T173000
UID:TALK16281AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/16281
DESCRIPTION:The spectral gap of a symmetric stochastic matrix
is the\nreciprocal of the best constant in its ass
ociated Poincare inequality. This\ninequality can
be formulated in purely metric terms\, where the m
etric is a\nHilbertian metric. This immediately al
lows one to define the spectral gap of\na matrix w
ith respect to other\, non-Euclidean\, geometries:
a standard\nprocedure which is used a lot in embe
dding theory\, most strikingly as a\nmethod to pro
ve non-embeddability in the coarse category. Motiv
ated by a\ncombinatorial approach to the construct
ion of bounded degree graph families\nwhich do not
admit a coarse embedding into any uniformly conve
x normed space\n(such spaces were first constructe
d by Lafforgue)\, we will naturally arrive\nat que
stions related to the behavior of non-linear spect
ral gaps under graph\noperations such as powering
and zig-zag products. We will also discuss the\nis
sue of constructing base graphs for these iterativ
e constructions\, which\nleads to new analytic and
geometric challenges.
LOCATION:MR4\, CMS
CONTACT:Ben Green
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